The smoothed finite element method (S-FEM): A framework for the design of numerical models for desired solutions

The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number o...

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Bibliographic Details
Published in:Frontiers of Structural and Civil Engineering 2019-04, Vol.13 (2), p.456-477
Main Author: Liu, Gui-Rong
Format: Article
Language:English
Subjects:
Automation
Cities
Civil Engineering
Computer simulation
Countries
Design
Domains
Engineering
Finite element analysis
Finite element method
Formulations
Locking
Mathematical models
Meshless methods
Nonlinear programming
Properties (attributes)
Regions
Review
Upper bounds
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Summary:The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects; 2) upper-bound solutions; 3) accurate solutions and higher convergence rates; 4) insensitivity to mesh distortion; 5) Jacobian-free; 6) volumetric-locking-free; and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on AI-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model on-demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.
ISSN:2095-2430
2095-2449
DOI:10.1007/s11709-019-0519-5